WASHINGTON — Leading senators working on immigration legislation reached a compromise Tuesday on the details of an expanded high-tech visa program, officials said as the Senate Judiciary Committee neared completion of its work on the measure.

At the same time, several officials said the White House has made it known to Sen. Patrick Leahy, the panel’s chairman, that it would prefer postponing a showdown over the rights of same sex spouses until a vote in the full Senate.

It was unclear whether Leahy would comply as he drives the committee toward a final vote on the sweeping immigration measure, which would give an estimated 11.5 million immigrants living in the United States illegally a chance at citizenship. “There have been 300 amendments offered. Why shouldn’t there be one more?” he told reporters.

At its core, the legislation would provide an opportunity of U.S. citizenship to millions of immigrants living in the country illegally, create a new visa program for low-skilled workers and permit a sizeable increase in the number of high-tech visas, at the same time it mandates new measures to crack down on future unlawful immigration.

Final committee approval is expected by midweek, with the full Senate likely to begin debate next month.

The compromise on high tech visas was negotiated by Sens. Orrin Hatch, R-Utah and Chuck Schumer, D-New York, and was designed to satisfy both industry, which relies increasingly on skilled foreign labor, and organized labor, which represents American workers.

Jeff Hauser, a spokesman for the AFL-CIO, said the organization remains opposed to the amendments, but will continue to support passage of the overall legislation with a path to citizenship.

The officials who confirmed the agreement did so on condition of anonymity because they were not authorized to speak publicly ahead of an official announcement.

As drafted, the bill would raise the current cap on so-called H-1B visas for highly skilled workers from 65,000 annually to 110,000, with the possibility of a further rise to 180,000. The legislation also included new protections designed to ensure American workers get the first shot at jobs, and high-tech firms objected to some of those constraints.

Hatch, whose state has a large high-tech industry, championed their cause. Schumer, an author of the bill, worked to satisfy his concerns. In exchange, Hatch told reporters Monday he’d committed to supporting the overall legislation when it comes to a vote in committee, lending it important GOP support.

The deal disclosed Tuesday modifies several amendments Hatch introduced on high-tech visas, including limiting some of the bill’s protections for U.S. workers to companies that are more heavily dependent on H-1B visas. That would exclude many major U.S. firms.

On the other major remaining unresolved issue, officials said there was a growing if unspoken expectation that the measure would likely emerge from committee without a provision granting same-sex spouses the same access to legal status as heterosexual spouses are entitled to.

Leahy has introduced a proposal to give equal treatment under the bill to same-sex couples, a provision gay rights groups seek. Several lobbyists and others noted during the day Monday that he had not said definitively that he would seek a vote on it before the panel completes its work, and neither the White House nor other Democrats on the committee have made a strong push for its inclusion.

Two people familiar with the deliberations said the White House had suggested to Leahy that it would be best to put the controversy until bill goes before the full Senate. They were not authorized to discuss the matter publicly and insisted on anonymity.

A vote on the proposal could create political difficulty for Democrats on the committee who support gay rights and are also members of the so-called Gang of Eight, which negotiated the main features of the legislation. That includes Schumer and Sen. Dick Durbin of Illinois.

Durbin has told outside groups he will back the change if it is offered. Schumer hasn’t said which way he would vote.

All eight authors of the bill have pledged to maintain the essential outlines of the legislation. A vote to add the gay rights provision could lead to approval on a party-line vote in committee, but lead to the collapse of Republican support on the Senate floor and the bill’s demise.

In addition, the Supreme Court is expected to issue a ruling by early July that could render the issue largely moot.

The measure is one of President Barack Obama’s top domestic priorities, although the administration has generally let the committee work on its own.

In a show of support, though, Obama and Vice President Joe Biden arranged to meet Tuesday in the Oval Office at the White House with individuals directly affected by the measure.